Hello,
The share of concurring votes (i.e. yes-yes and no-no) in total votes
between a pair of voters is a function of their ideological distance (index
continuous on [1,2]).
I show by other means that the votes typically are highly positively
correlated (with an average c=0.6). This is because voters sit together and
discuss the issue before taking a vote, but also because they share common
ideologies.
The coefficient is significant; sign correct; fit is good:
R-sq.(adj)=0.866.
BUT there seems to be a massive overdispersion:
Deviance explained=39.3%,
Residual deviance: 3874.0 on 102 degrees of freedom.
AND the residual-fitted plot shows heteroscedasticity.
The overdispersion cannot be remedied by regressing on LOG(index), or by
using the quasibinomial family with a scale parameter for the variance. The
estimated Dispersion parameter for quasibinomial family is large 37.34917.
QUESTION: Is there an overdispersion? Can overdispersion be due to
correlation between the votes? What can be done? The data is attached
below, "v1" concurring votes, "v0" dissenting votes, "idist" the index.
Thanks,
Serguei
DATA:
v1,v2,idist
376,40,1.125
328,88,1.375
367,49,1.145
372,44,1.125
273,143,1
325,91,1.125
375,41,1.125
357,59,1.375
751,359,1.885
816,294,1
752,358,1.885
829,281,1.3
857,253,1.05
759,351,1.07
848,262,1.135
803,307,1.385
555,555,1.885
346,70,1.5
381,35,1.27
398,18,1.25
289,127,1.125
1003,107,1
580,530,1.585
628,482,1.835
502,608,1.955
745,365,1.75
343,73,1.25
407,9,1.25
373,43,1.5
587,96,1.205
507,176,1.11
528,155,1.06
473,210,1.43
436,247,1.475
585,98,1.145
541,142,1.225
425,258,1.315
540,570,1.885
975,135,1.3
959,151,1.05
973,137,1.07
772,338,1.135
879,231,1.385
327,89,1.23
332,84,1.25
331,85,1.375
339,77,1.25
345,71,1.25
353,63,1
373,43,1.02
266,150,1.145
318,98,1.02
384,32,1.02
346,70,1.23
519,164,1.315
512,171,1.265
481,202,1.635
446,237,1.68
613,70,1.35
553,130,1.43
435,248,1.52
291,125,1.125
345,71,1
397,19,1
357,59,1.25
338,78,1.125
286,130,1.125
326,90,1.375
588,95,1.05
597,86,1.32
564,119,1.365
537,146,1.035
445,238,1.115
559,124,1.205
565,545,1.585
613,497,1.835
485,625,1.955
736,374,1.75
583,527,1.5
954,156,1.25
972,138,1.37
557,126,1.415
540,143,1.085
811,299,1.165
560,123,1.255
846,264,1.085
928,182,1.12
819,291,1.085
872,238,1.335
602,81,1.045
497,186,1.285
745,365,1.205
599,84,1.115
834,276,1.455
468,215,1.33
360,323,1.25
640,43,1.16
541,142,1.08
461,222,1.17
355,328,1.09
729,381,1.25
338,78,1
354,62,1.25
366,50,1.25
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